How to plot four sets of data

Question

a = RandomReal[{-1, 1}, 100];
b = RandomReal[{10, 20}, 100];
c = RandomReal[{100, 200}, 100];
d = RandomReal[{50, 60}, 100*100*100];

I have a simple program which generates 4 sets of data. Now I have to represent these data in a sensible way. The lists a, b and c as dimensions 1 $\times$ 100, and the dimension of d is $ 100^3 $.

We have a difficulty in representing anything beyond 3D space. How to make a sensible plot with these data? Is there anything Mathematica can offer for visualization?

Answer 1

ListDensityPlot3D

Combine a,b,c and d into a list of 4-tuples and use ListDensityPlot3D:

a = RandomReal[{-1, 1}, 100];
b = RandomReal[{10, 20}, 100];
c = RandomReal[{100, 200}, 100];
d = RandomReal[{50, 60}, {100*100*100, 1}];
abcd = Join[Tuples[{a, b, c}], d, 2];
ListDensityPlot3D[abcd, PlotLegends -> Automatic]

Graphics3D

Alternatively, you can use the rescaled version of d with the option VertexColors in Graphics3D:

d = RandomReal[{50, 60}, 100*100*100];
coords = Tuples[{a, b, c}];
colors = ColorData["TemperatureMap"] /@ Rescale[d];
Legended[Graphics3D[{Opacity[.1], Point[coords, VertexColors -> colors]}, 
  ImageSize -> 500, BoxRatios -> 1, Axes -> True], 
 BarLegend[{"TemperatureMap", {50, 60}}]]

BubbleChart

Finally, you can take a random sample of 4-tuples and use it with BubbleChart3D with bubble colors and sizes based on the last dimension of input data:

downsampled = RandomSample[abcd, 10000];
BubbleChart3D[downsampled, BubbleSizes -> {.01, .02}, 
 ChartStyle -> Opacity[.5], ColorFunction -> "TemperatureMap", 
 ChartLegends -> BarLegend[{"TemperatureMap", {50, 60}}]]